Application of First-order Shear Deformation Theory on Vibration Analysis of Stepped Functionally Graded Paraboloidal Shell with General Edge Constraints

The paper introduces a semi-analytical approach to analyze free vibration characteristics of stepped functionally graded (FG) paraboloidal shell with general edge conditions. The analytical model is established based on multi-segment partitioning strategy and first-order shear deformation theory. The displacement components along axial direction are represented by Jacobi polynomials, and the Fourier series are utilized to express displacement components in circumferential direction. Based on penalty method about spring stiffness technique, the general edge conditions of doubly curved paraboloidal shell can be easily simulated. The solutions about doubly curved paraboloidal shell were solved by approach of Rayleigh–Ritz. Convergence study about boundary parameters, Jacobi parameters et al. are carried out, respectively. The comparison with published literatures, FEM and experiment results show that the present method has good convergence ability and excellent accuracy.

Transition of Neural Signals on Adaptive Cylindrical Paraboloidal Shells

Cylindrical paraboloidal shells are common structures in communication systems, precision opto-mechanical systems and high-precision modern aerospace structures. Sensing is essential to validate the high performance of these modern structures. The purpose of this study is 1) to investigate microscopic neural signal generations from infinitesimal piezoelectric sensors over a cylindrical paraboloidal shell panel with curvature changes and 2) to determine the dominant signal component resulting from longitudinal or circumferential membrane strains and longitudinal or circumferential bending strains. Mathematical models of the cylindrical paraboloidal shells are presented first, followed by definition of the transverse mode shape function. Then, the microscopic signal generations of distributed sensors laminated on a cylindrical paraboloidal shell panel with simply-supported boundary conditions are investigated for three different cases: the ratio of meridian to radial distance of parabola at 1:4 (shallow), 1:1 (baseline) and 2:1 (deep). Analyzing these three cases suggests that as the shell changes from shallow to deep, 1) the circumferential membrane neural signals dominate more lower modes before the circumferential bending signals become dominant for n<m and the longitudinal bending signals become dominant for n>m as the mode increases and 2) the neural signals become localized where the curvature is small. Due to non-constant radius of curvature, these signal transitions on the cylindrical paraboloidal shells are rather unique, which has not been observed in other shells.

Distributed Modal Voltages of Nonlinear Paraboloidal Shells With Distributed Neurons

Effective health monitoring and distributed control of advanced structures depends on accurate measurements of dynamic responses of elastic structures. Conventional sensors used for structural measurement are usually add-on “discrete” devices. Lightweight distributed thin-film piezoelectric neurons fully integrated (laminated or embedded) with structural components can serve as in-situ sensors monitoring structure’s dynamic state and health status. This study is to investigate modal voltages and detailed signal contributions of linear or nonlinear paraboloidal shells of revolution laminated with piezoelectric neurons. Signal generation of distributed neuron sensors laminated on paraboloidal shells is defined first, based on the open-voltage assumption and Maxwell’s principle. The neuron signal of a linear paraboloidal shell is composed of a linear membrane component and a linear bending component; the signal of a nonlinear paraboloidal shell is composed of nonlinear and linear membrane components and a linear bending component due to the von Karman geometric nonlinearity. Signal components and distributed modal voltages of linear and nonlinear paraboloidal shells with various curvatures and thickness are investigated.